Given that l + m + n + o = 0, which of the given statements are true:

**(a)** l, m, n and o each must be a null vector.

**(b)** The magnitude of (l + n) equals the magnitude of (m+ o).

**(c)** The magnitude of l can never be greater than the sum of the magnitudes of m, n and o.

**(d)** m + n must lie in the plane of l and o if l and o are not collinear, and in the line of l and o, if they are collinear?

Asked by Pragya Singh | 1 year ago | 62

**Right answer is (a) False**

**Explanation:-**

In order to make l + m + n + o = 0, it is not necessary to have all the four given vectors to be null vectors.

There are other combinations which can give the sum zero.

**Right answer is (b) True**

**Explanation:-**

l + m + n + o = 0

l + n = – (m + o)

Taking mode on both the sides,

\(\left | l + n \right | = \left | -\left ( m + o \right ) \right | = \left | m + o \right |\)

Therefore, the magnitude of (l + n) is the same as the magnitude of (m + o).

**Right answer is (c) True**

**Explanation:-**

l + m + n + o = 0

l = (m + n + o)

Taking mode on both the sides,

**\(\left | l \right | = \left | m + n + o \right | \left | l \right | \leq \left | l \right | + \left | m \right | + \left | n \right |\) .......(i)**

Equation (i) shows the magnitude of l is equal to or less than the sum of the magnitudes of m, n and o.

**Right answer is (d) True**

**Explanation:-**

For,

l + m + n + o = 0

The resultant sum of the three vectors l, (m + n), and o can be zero only if (m + n) lie in a plane containing l and o, assuming that these three vectors are represented by the three sides of a triangle.

If l and o are collinear, then it implies that the vector (m + n) is in the line of l and o. This implication holds only then the vector sum of all the vectors will be zero.** **

**(a) **Show that for a projectile the angle between the velocity and the x-axis as a function of time is given by

\(\theta (t)=tan^{-1}(\dfrac{v_{0y-gt}}{v_{ox}})\)

**(b)** Shows that the projection angle θ_{0} for a projectile launched from the origin is given by

\(\theta_{0}=tan^{-1}(\dfrac{4h_{m}}{R})\)

where the symbols have their usual meaning

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A fighter plane flying horizontally at an altitude of 1.5 km with a speed of 720 km/h passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 m s^{-1} to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? (Take g = 10 m s^{-2} ).

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**(i)** a sphere

**(ii)** the length of a wire bent into a loop

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Clarify for the same.